Theresa May is being urged to clarify whether she is willing to meet the unplanned spending involved in policing the riots. Photograph: Paul Ellis/AFP/Getty Images

Concern is growing among senior police officers that the Home Office will not guarantee all the extra costs of policing last week's riots, leading figures in the Labour party have warned.

The home secretary, Theresa May, is being asked to urgently clarify whether she is willing to meet all the unplanned spending involved in quelling the riots, including the costs of overtime, cancelling leave and drafting in officers from other forces around the country.

The dispute comes as the chairmen of some police authorities across England expressed anger over May's criticism on Tuesday that they had proved to be "unaccountable, unelected and invisible" during last week's riots.

Nottinghamshire police have said they face a bill of £1.2m for the extra policing and the repair costs to five police stations that came under attack last Tuesday.

At the end of last week neighbouring Leicestershire police said they were likely to have spent at least £250,000 on their operation – many officers were working 12-hour days instead of the normal working hours – but no other forces have so far issued figures for the final costs they face.

The former Labour policing minister Vernon Coaker has written to the home secretary, seeking urgent clarification on the level of government support for police forces.

He has also expressed fears that part of the bill for the exceptional costs of the riots will have to come out of police budgets which are already facing 20% cuts.

In last week's Commons emergency debate, David Cameron gave the impression that the Treasury reserve would be used to meet the operational costs of policing the riots.

But May has since made it clear that other arrangements are to be used and each force is being asked to apply for a special grant. This scheme has been used in the past to meet exceptional costs, such as policing party conferences, but usually falls short of meeting the entire bill.

Labour sources say they have been contacted this week by senior police officers deeply concerned over how the extra costs are going to be met, and the impact this may have on their own budgets and operational capacity if there are further disturbances in the coming weeks.

"I hope you will agree with me that it would be shocking and unacceptable if the cost of public order policing in the riots, given current police budgets, ended up cutting other vital police work, including neighbourhood policing or detective work that is vital in preventing future outbreaks of violence," Coaker, the shadow policing minister, said. "Can you guarantee this will not happen?"

He urged the home secretary to publish a full force-by-force breakdown of the costs of policing the riots, including extra overtime, and to confirm that the Home Office or Treasury would meet them in full.

A Home Office spokesman said: "There is already an established system of special grants in place to support forces where they face unexpected or exceptional costs.

"It is up to individual forces if they wish to apply for a special grant, and all applications will be considered. The government has made clear that it will support the police."

The dispute comes as the Association of Police Authorities published an open letter to May, rejecting as "untrue and inaccurate" her comments contrasting the active role of Boris Johnson, the London mayor, on the streets of London with the "unaccountable, unelected and invisible police authority chairmen in other parts of the country".

The APA said: "This unevidenced, Londoncentric assertion was either regretfully ill-informed or wilfully inaccurate. In either case, we believe it to be unbecoming of a secretary of state.

"It has caused not only bemusement but anger amongst police authorities and our partners across the country.

"Quite simply, your allegations are completely untrue and a cursory conversation with the relevant chief constables, council leaders or representatives of local media could have confounded it."

Bishop Derek Webley, the chairman of the West Midlands police authority, said he had taken May's comments as a personal insult as he and many members of his authority had worked tirelessly behind the scenes. He said visibility was not just about seeking celebrity in the media.

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